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Corresponding Author: Murat Sat, Department of Mathematics, Faculty of Science and Art, Erzincan University, Erzincan, 24100, Turkey 1571 On an Inverse Spectral Problem for an Integro-differential Operator Etibar S. Panakhov and Murat Sat Department of Mathematics, Faculty of Science, Firat University, Elazig, 23119, Turkey Department of Mathematics,… (More)

- Hikmet Koyunbakan, Etibar S. Panakhov
- Mathematical and Computer Modelling
- 2006

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set. c © 2006 Elsevier Ltd. All rights reserved.

It is well known that the two spectra {λn} and {μn} uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type ( ) 2 1 2 r r + + (where is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the… (More)

- Erdal Bas, Resat Yilmazer, Etibar Panakhov
- TheScientificWorldJournal
- 2013

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

The inverse nodal problem for the Sturm–Liouville operator is the problem of finding the potential function q and the boundary conditions using the nodal points. The purpose of this paper is to present a method for solving the inverse nodal problem for a singular differential operator on a finite interval. We find asymptotic formulas for nodal points and… (More)

and Applied Analysis 3 and asymptotic formulas for large argument JV (x) = √ 2 πx {cos [x − Vπ 2 − π 4 ] + O( 1 x )} , J V (x) = − √ 2 πx {sin [x − Vπ 2 − π 4 ] + O( 1 x )} . (23) It can be shown [19] that there exists a kernel H(x, t)(?̃?(x, t)) continuous in the triangle 0 ≤ t ≤ x ≤ 1 such that by using the transformation operator every solution of… (More)

- Hikmet Koyunbakan, Etibar S. Panakhov
- Mathematical and Computer Modelling
- 2008

In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt’s theorem concerning the structure of the difference q(x) − q̃(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin2 x at the points 0… (More)

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